Asymmetric Multidimensional Scaling of Brand Switching Among Margarine Brands

Abstract

Brand switching data among 12 margarine brands were analyzed by the asymmetric multidimensional scaling based on the singular value decomposition. A two-dimensional result was adopted as the solution. A configuration based on the left and right singular vectors is given along each dimension. The left singular vector represents an outward tendency of switching from the corresponding brand to the other brands, and the right singular vector represents an inward tendency of being switched to the corresponding brand from the other brands. The configuration along Dimension 1 shows that the three brands with the larger market share compete vigorously with each other. The configuration along Dimension 2 classifies 12 brands into two groups; the brand switching between two groups is small, while that within each group is large.

Visualization of cross‐resistance between antimicrobial agents by asymmetric multidimensional scaling

“…MDS has been used in psychology, sociology and marketing. [6][7][8] In the medical field, MDS has been used to show the (dis)similarity of individual organisms, such as viruses and cancer cells, from DNA sequences and clinical information. [9][10][11][12] By considering the CRR matrix as the accumulation of asymmetric similarity data, we applied the analytical method developed by Okada and Imaizumi, "asymmetric MDS based on the distance-radius model," 13 to the analysis of the CRR matrix.…”

“…MDS has been used in psychology, sociology and marketing. 6 , 7 , 8 In the medical field, MDS has been used to show the (dis)similarity of individual organisms, such as viruses and cancer cells, from DNA sequences and clinical information. 9 , 10 , 11 , 12 …”

Unfolding Models for Asymmetric Dissimilarity Data With External Information Based on Path Structures

“…In the brand switchingdata,theelementfrombranditojindicatesfrequencyofbuyingbrandjafterbuyingbrand iforcustomers.Torevealthecompetitiverelationsamongbrands,AsymmetricMultidimensional Scaling (AMDS) is applied to the brand switching data (e.g. Okada and Tsurumi, 2012), where AMDSisvisualizationmethodfortheasymmetricrelationsforsubjects.Inusually,brandswitching dataisgeneratedfromPOSdata.Therefore,wecanusuallygetthemultivariatedataasexternal informationforthesamesubjectsalongwiththebrandswitchingdatafromthePOSdata.However, insuchthesituation,ordinalAMDSprovideonlytheinterpretationofasymmetricrelations,notthe relationbetweentheasymmetriesandtheexternalinformation.IftheestimatedaxesinAMDScanbe interpretedasthoseinPrincipalComponentAnalysis(PCA),thevisualizationresultisveryuseful. Therefore,weproposenewAMDSwithexternalinformation.…”